Solve u^-5*u^7*u^-3

$$u ^ { - 5 } \cdot u ^ { 7 } \cdot u ^ { - 3 }$$

Evaluate

$$\frac{1}{u}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$u^{-5}u^{7}u^{-3}$$

Use the Multiplication Rule for Exponents.

$$u^{-5+7-3}$$

Add the exponents -5 and 7.

$$u^{2-3}$$

Add the exponents 2 and -3.

$$\frac{1}{u}$$

Differentiate w.r.t. u

$$-\frac{1}{u^{2}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -5 and 7 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{2}u^{-3})$$

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{-1})$$

The derivative of ax^{n} is nax^{n-1}.

$$-u^{-1-1}$$

Subtract 1 from -1.

$$-u^{-2}$$